Discretizing Continuous Time Series for Imputation with Masked Diffusion Training

TL;DR

MDTIM model discretizes time series for imputation, achieving 30% accuracy improvement.

cs.LG 🔴 Advanced 2026-08-20 4 views
Dongbin Kim Seungyun Lee Geonwoo Shin Jaewook Lee
time series imputation discretization diffusion model machine learning

Key Findings

Methodology

MDTIM uses masked diffusion and stochastic discretization to map continuous time series to discrete tokens, achieving precise imputation through expectation decoding. The model structure includes a factorized temporal-variate transformer combined with spectral consistency loss.

Key Results

  • MDTIM achieves a MAE of 0.044 on the Energy dataset, outperforming CSDI's 0.094, showcasing robustness under complex missing patterns.
  • On the ETTh dataset, MDTIM achieves a MAE of 0.127 at 30% missing rate, significantly better than FGTI's 0.218.
  • MDTIM excels on the PhysioNet 2012 dataset with a MAE of 0.236, leading SAITS's 0.283.

Significance

This study addresses structural separation in time series imputation through innovative discretization, significantly improving accuracy and robustness, with important implications for academia and industry.

Technical Contribution

MDTIM introduces stochastic discretization and spectral consistency loss, overcoming limitations of existing diffusion models, achieving more precise time series imputation, offering new theoretical guarantees and engineering possibilities.

Novelty

MDTIM is the first to apply masked diffusion to time series imputation, using stochastic discretization to maintain sequence continuity, showing significant innovation compared to existing methods.

Limitations

  • In extreme missing scenarios, the model may fail to accurately recover the original signal.
  • High computational cost for high-dimensional data.

Future Work

Future work could explore MDTIM's application to more complex time series data and optimize computational efficiency.

AI Executive Summary

Time series imputation is a critical task in data analysis, yet existing methods struggle with complex dynamics and noise. The MDTIM model addresses structural separation and noise prediction issues through masked diffusion and stochastic discretization techniques. The model employs a factorized temporal-variate transformer and integrates spectral consistency loss for precise imputation. Experimental results demonstrate MDTIM's superiority over existing baselines across multiple datasets, showcasing robustness under complex missing patterns. This study not only improves imputation accuracy but also provides new perspectives and methods for time series analysis. Future work will further optimize the model's computational efficiency and explore its application to more complex data.

Deep Analysis

Background

Time series imputation is crucial for recovering original signals from partially observed data. Existing methods like RNNs and Transformers struggle with long-range dependencies and complex dynamics, while diffusion models like CSDI focus on noise prediction.

Core Problem

Existing imputation methods face challenges in structural separation of missing and observed values, and continuous diffusion models typically predict noise rather than original signals, leading to decreased imputation accuracy.

Innovation

MDTIM achieves structural separation and precise imputation through masked diffusion and stochastic discretization. Masked diffusion replaces missing values with special symbols, while stochastic discretization maintains sequence continuity.

Methodology

  • �� Masked diffusion: Replace missing values with [MASK] symbols, directly predict original values. • Stochastic discretization: Map continuous values to discrete tokens, inject noise to retain information. • Factorized transformer: Alternately process time and variable axes, capture long-range dependencies. • Spectral consistency loss: Ensure global temporal consistency.

Experiments

Experiments conducted on Energy, ETTh, Weather datasets with varying missing rates and masking mechanisms. Baselines include RNN, Transformer, and diffusion models, evaluating imputation accuracy and robustness.

Results

MDTIM achieves a MAE of 0.044 on the Energy dataset, outperforming CSDI's 0.094, and excels on the ETTh dataset with a MAE of 0.127. The model also performs well on the PhysioNet 2012 dataset.

Applications

MDTIM can be used for sensor fault data recovery, financial market analysis, enhancing data analysis accuracy and reliability.

Limitations & Outlook

The model may perform poorly in extreme missing scenarios, with high computational costs, requiring further optimization.

Plain Language Accessible to non-experts

Imagine you're cooking in a kitchen, where ingredients represent time series data, and some ingredients are missing. MDTIM acts like a smart chef, observing the existing ingredients and cooking steps to infer what the missing ingredients are and add them back. It uses a special method to ensure that even with incomplete ingredients, the final dish is still delicious.

ELI14 Explained like you're 14

Hey there, imagine you're playing a puzzle game but some pieces are missing. MDTIM is like a super smart puzzle master who can guess what the missing pieces look like based on the remaining ones and fill them in. This way, your puzzle is complete! Isn't that cool?

Glossary

Masked Diffusion Model

A model that replaces missing values with special symbols and predicts original values.

Used in time series imputation tasks for structural separation.

Stochastic Discretization

A method to map continuous values to discrete tokens and inject noise to retain information.

Used to maintain time series continuity.

Factorized Transformer

A transformer structure that alternately processes time and variable axes.

Used to capture long-range dependencies.

Spectral Consistency Loss

A loss function ensuring global temporal consistency.

Used to maintain frequency structure of time series.

Expectation Decoding

A method to compute continuous values from predicted probability distributions.

Used for precise imputation.

Open Questions Unanswered questions from this research

  • 1 How to further optimize MDTIM's computational efficiency for larger datasets?
  • 2 How to improve model accuracy in extreme missing scenarios?

Applications

Immediate Applications

Sensor Fault Data Recovery

MDTIM can be used to recover data lost due to sensor faults, enhancing data analysis accuracy.

Financial Market Analysis

Through precise imputation, MDTIM can be used to analyze financial market data and predict trends.

Long-term Vision

Complex Dynamic System Monitoring

MDTIM can be applied to real-time monitoring of complex dynamic systems, providing more reliable data support.

Abstract

Time series imputation is a crucial area for reliable time series analysis, yet it remains challenging due to the complex temporal dynamics and noise of real-world data. Existing approaches, however, exhibit two limitations: missing and observed values are embedded within the same representation space without explicit structural separation, and continuous diffusion-based methods are trained to predict added noise rather than the original signal. To address these, we propose the Masked Diffusion Time-series Imputation Model (MDTIM), which leverages the training paradigm of masked diffusion model for imputation tasks. The MASK token is structurally orthogonal to valid observations, and the model directly predicts the original values, naturally aligning both the representation and the learning objective with the imputation task. To bridge the gap between discrete masked diffusion and the continuous, ordinal nature of time series, we further introduce Stochastic Discretization, which maps continuous values to ordinal-aware tokens while preserving continuous dynamics. Our experiments on diverse benchmarks confirm that MDTIM achieves superior robustness and scalability, consistently outperforming state-of-the-art deterministic and generative baselines across various missing scenarios.

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